For the vertical linear complementarity problem (VLCP), by converting it to the equivalent absolute value equation containing the minimum function, we present a new modulus-based matrix splitting method to gain its numerical solution, coincidentally, which covers the classical modulus-based matrix splitting (MMS) method. Under the mild conditions, the convergence conditions of the proposed method are gained. The presented convergence conditions not only ensure the convergence of the proposed method, but also cover or improve some existing results for the above classical MMS method. By leveraging some numerical experiments from the discrete Hamilton-Jacobi-Bellman equation, we confirm the efficiency of the proposed method. Numerical results confirm that the proposed method overmatches other state-of-the-art methods in terms of computation time, such as the single-step smooth Newton method and the projected fixed-point iteration method.
Li et al. (Fri,) studied this question.